Synchronization Fronts in a Spatially Extended System of Hybrid Rayleigh-van der Pol Oscillators
Abstract
Numerous biological systems exhibit transitions to synchronised oscillations via a population-density-dependant mechanism known as quorum sensing. Here we propose a model system, based on spatially distributed limit-cycle oscillators, that allows us to capture the dynamics of synchronization fronts by taking the continuum limit as the number of coupled oscillators tends to infinity. We explore analytically a family of wavefront-type solutions to the system in terms of model parameters and corroborate its validity via a numerical finite-difference method algorithm. Finally, we review our results in light of some experimental systems in synthetic biology based on a synchronised quorum of genetic clocks, coupled via a diffusive auto-inducer signalling molecule analogue to our Hooke-like coupling scheme within the proposed hybrid Rayleigh-van der Pol model.
Keywords
Cite
@article{arxiv.2208.09119,
title = {Synchronization Fronts in a Spatially Extended System of Hybrid Rayleigh-van der Pol Oscillators},
author = {Carles Tardío Pi and Jorge Castillo Medina and Pablo Padilla Longoria},
journal= {arXiv preprint arXiv:2208.09119},
year = {2022}
}